A system with input x[n] and output y[n] is given as $$y\left( n \right) = \left( {\sin {5 \over 6}\pi n} \right)x\left( n \right).$$ The system is

The correct answer is: A. Linear, stable and invertible

A linear system is a system in which the output is a linear combination of the inputs. A stable system is a system that does not amplify the input signal. An invertible system is a system that can be inverted, i.e., the output can be recovered from the input.

The given system is linear because the output is a linear combination of the inputs. The system is stable because the output does not grow without bound as the input increases. The system is invertible because the output can be recovered from the input by multiplying the output by the inverse of the system function.

Here is a brief explanation of each option:

• Option A: Linear, stable and invertible

This is the correct answer. The system is linear because the output is a linear combination of the inputs. The system is stable because the output does not grow without bound as the input increases. The system is invertible because the output can be recovered from the input by multiplying the output by the inverse of the system function.

• Option B: Non-linear, stable and non-invertible

This option is incorrect. The system is linear because the output is a linear combination of the inputs. However, the system is not invertible because the output cannot be recovered from the input by multiplying the output by the inverse of the system function.

• Option C: Linear, stable and non-invertible

This option is incorrect. The system is linear because the output is a linear combination of the inputs. However, the system is not stable because the output grows without bound as the input increases.

• Option D: Linear, unstable and invertible

This option is incorrect. The system is linear because the output is a linear combination of the inputs. However, the system is not stable because the output grows without bound as the input increases.